Showing papers on "Discretization published in 1988"
TL;DR: A polynomial-based discretization scheme is constructed around a technique called ‘curvature compensation’; the resultant curvature-compensated convective transport approximation is essentially third-order accurate in regions of the solution domain where the concept of order is meaningful.
Abstract: The paper describes a new approach to approximating the convection term found in typical steady-state transport equations. A polynomial-based discretization scheme is constructed around a technique called ‘curvature compensation’; the resultant curvature-compensated convective transport approximation is essentially third-order accurate in regions of the solution domain where the concept of order is meaningful. In addition, in linear scalar transport problems it preserves the boundedness of solutions. Sharp changes in gradient in the dependent variable are handled particularly well. But above all, the scheme, when used in conjunction with an ADI pentadiagonal solver, is easy to implement with relatively low computational cost, representing an effective algorithm for the simulation of multi-dimensional fluid flows. Two linear test problems, for the case of transport by pure convection, are employed in order to assess the merit of the method.
824 citations
TL;DR: A well-posed variational formulation results from the use of a controlled-continuity surface model, and Finite-element shape primitives yield a local discretization of the variational principle, which is an efficient algorithm for visible-surface reconstruction.
Abstract: A computational theory of visible-surface representations is developed. The visible-surface reconstruction process that computes these quantitative representations unifies formal solutions to the key problems of: (1) integrating multiscale constraints on surface depth and orientation from multiple-visual sources; (2) interpolating dense, piecewise-smooth surfaces from these constraints; (3) detecting surface depth and orientation discontinuities to apply boundary conditions on interpolation; and (4) structuring large-scale, distributed-surface representations to achieve computational efficiency. Visible-surface reconstruction is an inverse problem. A well-posed variational formulation results from the use of a controlled-continuity surface model. Discontinuity detection amounts to the identification of this generic model's distributed parameters from the data. Finite-element shape primitives yield a local discretization of the variational principle. The result is an efficient algorithm for visible-surface reconstruction. >
520 citations
Book•
01 Jul 1988
TL;DR: Numerical computation of internal and external flows fundamentals of numerical discretization PDF is available at the online library.
Abstract: NUMERICAL COMPUTATION OF INTERNAL AND EXTERNAL FLOWS FUNDAMENTALS OF NUMERICAL DISCRETIZATION PDF Are you looking for numerical computation of internal and external flows fundamentals of numerical discretization Books? Now, you will be happy that at this time numerical computation of internal and external flows fundamentals of numerical discretization PDF is available at our online library. With our complete resources, you could find numerical computation of internal and external flows fundamentals of numerical discretization PDF or just found any kind of Books for your readings everyday.
512 citations
TL;DR: In this article, operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations: singular integrals (power and logarithmic singularities, finite part...
Abstract: Operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations: singular integrals (power and logarithmic singularities, finite part ...
494 citations
TL;DR: In this paper, the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature, is dealt with with the aid of the finite element method.
Abstract: With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. The spatial variabilities are modeled as two‐dimensional stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. Then, the present paper takes advantage of the Neumann expansion technique in deriving the finite element solution for the response variability within the framework of the Monte Carlo method. The Neumann expansion technique permits more detailed comparison between the perturbation and Monte Carlo solutions for accuracy, convergence, and computational efficiency. The result from such a Monte Carlo method is also compared with that based on the commonly used perturbation method. The comparison shows that the validity of the perturbation method is limited to the c...
480 citations
TL;DR: This paper provides a detailed exposition of model construction, structural stability of constructed models, stability of the scheme, etc, and considers the relationship between the CDS modeling and the conventional description in terms of partial differential equations, which leads to a new discretization scheme for semilinear parabolic equations.
Abstract: We present a computationally efficient scheme of modeling the phase-ordering dynamics of thermodynamically unstable phases. The scheme utilizes space-time discrete dynamical systems, viz., cell dynamical systems (CDS). Our proposal is tantamount to proposing new Ansa$iuml---tze for the kinetic-level description of the dynamics. Our present exposition consists of two parts: part I (this paper) deals mainly with methodology and part II [S. Puri and Y. Oono, Phys. Rev. A (to be published)] gives detailed demonstrations. In this paper we provide a detailed exposition of model construction, structural stability of constructed models (i.e., insensitivity to details), stability of the scheme, etc. We also consider the relationship between the CDS modeling and the conventional description in terms of partial differential equations. This leads to a new discretization scheme for semilinear parabolic equations and suggests the necessity of a branch of applied mathematics which could be called ``qualitative numerical analysis.''
427 citations
TL;DR: In this paper, the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear Stochastic Differential Equations of the generalized Ito type (containing both jump and diffusion components) is considered.
Abstract: This paper considers the parametric estimation problem for continuous-time stochastic processes described by first-order nonlinear stochastic differential equations of the generalized Ito type (containing both jump and diffusion components). We derive a particular functional partial differential equation which characterizes the exact likelihood function of a discretely sampled Ito process. In addition, we show by a simple counterexample that the common approach of estimating parameters of an Ito process by applying maximum likelihood to a discretization of the stochastic differential equation does not yield consis
311 citations
TL;DR: A comparison of various iterative solvers for the Stokes problem, based on the preconditioned Uzawa approach is devoted, to prove the quality of these schemes, whose discretization is detailed.
Abstract: SUMMARY This paper is devoted to a comparison of various iterative solvers for the Stokes problem, based on the preconditioned Uzawa approach. In the first section the basic equations and general results of gradient-like methods are recalled. Then a new class of preconditioners, whose optimality will be shown, is introduced. In the last section numerical experiments and comparisons with multigrid methods prove the quality of these schemes, whose discretization is detailed.
269 citations
05 Dec 1988
TL;DR: The optimization problem is set up as a discrete multi-stage decision process and is solved by a “time-delayed” discrete dynamic programming algorithm, which leads to a stable behavior for the active contours over iterations, in addition to allowing for hard constraints to be enforced on the behavior of the solution.
Abstract: Energy-Minimizing Active Contour Models (snakes) have recently been proposed by Kass et al. [8] as a top-down mechanism for locating features of interest in images. The Kass et al.’s algorithm involves four steps: setting up a variational integral on the continuous plane, deriving a pair of Euler equations, discretizing them, and solving the discrete equations iteratively until convergence. This algorithm suffers from a number of problems. We discuss these problems and present an algoIithm for active contours based on dynamic programming. The optimization problem is set up as a discrete multi-stage decision process and is solved by a “time-delayed” discrete dynamic programming algorithm. This formulation leads to a stable behavior for the active contours over iterations, in addition to allowing for hard constraints to be enforced on the behavior of the solution. Results of the application of the proposed algorithm to real images is presented.
267 citations
TL;DR: The solution of the Stokes problem is approximated by three stabilized mixed methods, one due to Hughes, Balestra, and Franca and the other two being variants of this procedure.
Abstract: The solution of the Stokes problem is approximated by three stabilized mixed methods, one due to Hughes, Balestra, and Franca and the other two being variants of this procedure. In each case the bilinear form associated with the saddle-point problem of the standard mixed formulation is modified to become coercive over the finite element space. Error estimates are derived for each procedure.
260 citations
01 Jan 1988
TL;DR: In this article, the random walk method is used for the case of an ideal tracer starting out from the Ito-Fokker-Planck equation. But the method suffers from the general roughness of simulated distributions in space and time due to statistical fluctuations and resolution problems.
Abstract: Standard finite difference and finite element solution methods of the pollutant transport equation require restrictive spatial discretization in order to avoid numerical dispersion. The random walk method offers a robust alternative if for reasons of calculational effort discretization requirements cannot be met. The method is discussed for the case of an ideal tracer starting out from the Ito-Fokker-Planck-equation. Features such as chemical reactions and adsorption can be incorporated. Besides being an alternative to other solution methods for the classical transport equation the random walk deserves attention due to its generalizability allowing the incorporation of non-Fickian dispersion. A shortcoming of the method results from the general roughness of simulated distributions in space and time due to statistical fluctuations and resolution problems. The method is applied to a field case of groundwater pollution by chlorohydrocarbons.
01 Jan 1988
TL;DR: In this article, a simulation of the flow about the integrated space shuttle vehicle in ascent mode has been undertaken for various flight conditions using the Chimera composite grid discretization approach, and an implicit approximately factored finite-difference procedure was used to solve the three-dimensional thin-layer Navier-Stokes equations.
Abstract: A simulation of the flow about the integrated space shuttle vehicle in ascent mode has been undertaken for various flight conditions using the Chimera composite grid discretization approach. Overset body-conforming grids were used to represent each geometric component, and an implicit approximately factored finite-difference procedure was used to solve the three-dimensional thin-layer Navier-Stokes equations. The computational results have been compared with both wind tunnel and flight test data. Although relatively good agreement is obtained with the experimental data, further refinement and evaluation of numerical error is under way.
01 Jan 1988
TL;DR: In this article, numerique and ecoulement are used for CFD reference records. But the reference record was created on 2005-11-18, modified on 2016-08-08.
Abstract: Keywords: numerique ; ecoulement ; CFD Reference Record created on 2005-11-18, modified on 2016-08-08
TL;DR: Methods for multirate digital control system design, sampling rate selection, discretization, and synthesis methods are applied to two example design problems andMultirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load.
Abstract: Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The successive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load. >
TL;DR: In this article, a control-theoretic approach is used to design a new automatic stepsize control algorithm for the numerical integration of ODE's, which is more robust at little extra expense.
Abstract: A control-theoretic approach is used to design a new automatic stepsize control algorithm for the numerical integration of ODE's. The new control algorithm is more robust at little extra expense. Its improved performance is particularly evident when the stepsize is limited by numerical stability. Comparative numerical tests are presented.
TL;DR: In this paper, a set of natural design variables are chosen as the design variables defining the shape of a structure, and the displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape.
Abstract: The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of ‘control’ nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.
TL;DR: It is proved that the only non-trivial conformal mapping which exists between the two spheres is based on the transformation introduced by Schmidt, but the Pole of the collocation grid has no longer to coincide with the pole of dilatation.
Abstract: We follow the approach suggested by F. Schmidt to implement a spectral global shallow-water model with variable resolution. A conformal mapping is built between the earth and a computational sphere and the equations are discretized on the latter using the standard spectral technique associated with a collocation (Gaussian) grid. We prove that the only non-trivial conformal mapping which exists between the two spheres is based on the transformation introduced by Schmidt, but the pole of the collocation grid has no longer to coincide with the pole of dilatation. We implement the technique in an explicit model, where only minor modifications to a uniform resolution model are needed. The semi-implicit scheme and the nonlinear normal mode initialization are proved to work satisfactorily. 24-hour forecasts show that the method is successful in dealing with the shallow-water equations and allow us to discuss the potential of the approach.
TL;DR: In this paper, the authors studied phase-locking in a network of coupled nonlinear oscillators with local interactions and random intrinsic frequencies and derived an exact expression for the probability of phase locking in a linear chain of such oscillators.
TL;DR: In this article, the error analysis of finite element Galerkin approximation of the nonstationary Navier-Stokes equations was carried out for higher order finite elements under appropriate assumptions about the smoothness and stability of the solution.
Abstract: This paper continues our error analysis of finite element Galerkin approximation of the nonstationary Navier–Stokes equations. Optimal order error estimates, both local and global, are derived for higher order finite elements under appropriate assumptions about the smoothness and stability of the solution. These assumptions take into account the loss of regularity at $t = 0$ that one generally has to expect in the absence of higher order nonlocal compatibility conditions for the data of the problem.
TL;DR: A discretization scheme is applied to the hydrodynamic model for semiconductor devices that generalizes the Scharfetter-Gummel method to both the momentum-conservation and the energy-cons conservation equations, providing a satisfactory description of such effects as velocity overshoot and carrier heating.
Abstract: A discretization scheme is applied to the hydrodynamic model for semiconductor devices that generalizes the Scharfetter-Gummel method to both the momentum-conservation and the energy-conservation equations. The major advantages of the scheme are: (1) the discretization is carried out without neglecting any terms, thus providing a satisfactory description of such effects as velocity overshoot and carrier heating; and (2) the resulting equations lend themselves to a self-consistent solution procedure similar to those currently used to solve the simpler drift-diffusion equations. Two-dimensional steady-state simulations of an n-channel MOSFET and of an n-p-n BJT (bipolar junction transistor) have been carried out by means of an improved version of the program HFIELDS. Carrier-temperature plots have been obtained with a reasonable computational effort, demonstrating the efficiency of this technique. The results have been compared with those obtained with the standard drift-diffusion model and significant differences in the electron concentration have been found, especially at the drain end of the MOSFET channel. >
Book•
01 Jan 1988
TL;DR: This research attacked the mode confusion problem by developing a modeling framework called CFD Monte Carlo Monte Carlo simulation (CfD) to describe the “magnitude of the Monte Carlo errors”.
Abstract: Keywords: numerique ; ecoulement ; CFD Reference Record created on 2005-11-18, modified on 2016-08-08
TL;DR: A method is considered for the integration in time of a partial integro-differential equation using the discretization technique patterned after the idea of Ch.
Abstract: A method is considered for the integration in time of a partial integro-differential equation. The discretization technique employed is patterned after an idea of Ch. Lubich. Error bounds are derived for both smooth and nonsmooth initial data.
TL;DR: In this article, a general calculation procedure for computing fluid flow and related phenomena in arbitrary-shaped domains is presented, based on a control-volume approach with a staggered grid arrangement, which avoids any reference to the differential form of the governing equations for the covariant velocity components.
Abstract: A general calculation procedure for computing fluid flow and related phenomena in arbitrary-shaped domains is presented. The scheme has been developed for a generalized nonorthogonal coordinate system and is based on a control-volume approach with a staggered grid arrangement. The physical covariant velocity components are selected as the dependent variables in the momentum equations. The discretization equations for these velocity components are obtained by an algebraic manipulation of the discretization equations for the Cartesian velocity components. Such a practice avoids any reference to the differential form of the governing equations for the covariant velocity components. The coupling between the continuity and momentum equations is effected using the SIMPLER algorithm.
01 Jun 1988
TL;DR: In this paper, a multigrid (MG) method for the approximation of steady solutions to the full 2D Euler equations is described, and the space discretization is obtained by the finite volume technique and Osher's approximate Riemann-solver.
Abstract: A multigrid (MG) method for the approximation of steady solutions to the full 2-D Euler equations is described. The space discretization is obtained by the finite volume technique and Osher’s approximate Riemann-solver. Symmetric Gauss-Seidel relaxation is applied to solve the nonlinear discrete system of equations. A multigrid method, the full approximation scheme, accelerates this iterative process.
TL;DR: In this paper, a discretized model is set up in which both patient section and radiation field are fine-discretized, which leads to a linear feasibility problem, which is solved by a relaxation method.
TL;DR: In this paper, an effective formulation for computing design sensitivities required in the shape optimization of solid objects using the boundary element method (BEM) is described, resulting in a general and efficient analysis technique for design sensitivity of all structural quantities.
Abstract: This paper describes an effective formulation for computing design sensitivities required in the shape optimization of solid objects using the boundary element method (BEM). Implicit differentiation of the discretized boundary integral equations is performed, resulting in a general and efficient analysis technique for design sensitivities of all structural quantities. The numerical integration of kernels is performed, which involves the products of shape functions, fundamental solutions, and their derivatives required for sensitivity calculations. The sensitivities of all components of the boundary stress tensor are obtained without additional numerical integrations. High‐order elements with curved sides are employed for stress and sensitivity analysis. A multizone analysis is implemented and its computational advantages are studied. An approximate method for design sensitivity calculations is also suggested and its performance and computational economy relative to the exact procedure are presented. Compa...
TL;DR: In this paper, a new mixed variational formulation for linear elasticity was proposed, which does not require symmetric tensors and therefore is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.
Abstract: We propose a new mixed variational formulation for the equations of linear elasticity. It does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.
01 Oct 1988
TL;DR: A new nonconforming discretizatio_l which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement and constitutes a new approach to discretization-driven ,[omain decomposition.
Abstract: Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.
TL;DR: A new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages and is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence.
Abstract: A new computational algorithm is presented for the solution of discrete time linearly constrained stochastic optimal control problems decomposable in stages. The algorithm, designated gradient dynamic programming, is a backward moving stagewise optimization. The main innovations over conventional discrete dynamic programming (DDP) are in the functional representation of the cost-to-go function and the solution of the single-stage problem. The cost-to-go function (assumed to be of requisite smoothness) is approximated within each element defined by the discretization scheme by the lowest-order polynomial which preserve its values and the values of its gradient with respect to the state variables at all nodes of the discretization grid. The improved accuracy of this Hermitian interpolation scheme reduces the effect of discretization error and allows the use of coarser grids which reduces the dimensionality of the problem. At each stage, the optimal control is determined on each node of the discretized state space using a constrained Newton-type optimization procedure which has quadratic rate of convergence. The set of constraints which act as equalities is determined from an active set strategy which converges under lenient convexity requirements. This method of solving the single-stage optimization is much more efficient than the conventional way based on enumeration or iterative methods with linear rate of convergence. Once the optimal control is determined, the cost-to-go function and its gradient with respect to the state variables is calculated to be used at the next stage. The proposed technique permits the efficient optimization of stochastic systems whose high dimensionality does not permit solution under the conventional DDP framework and for which successive approximation methods are not directly applicable due to stochasticity. Results for a four-reservoir example are presented. The purpose of this paper is to present a new computational algorithm for the stochastic optimization of sequential decision problems. One important and extensively studied class of such problems in the area of water resources is the discrete time optimal control of multireservoir systems under stochastic inflows. Other applications include the optimal design and operation of sewer systems [e.g., Mays and Wenzel, 1976; Labadie et al., 1980], the optimal conjunctive utilization of surface and groundwater resources [e.g., Buras, 1972], and the minimum cost water quality maintenance in rivers [e.g., Dracup and Fogarty, 1974; Chang and Yeh, 1973], to mention only a few of the water resources applications and pertinent references. An extensive review of dynamic programming applications in water resources can be found in the works by Yakowitz [1982] and Yeh [1985]. Before we proceed with the
TL;DR: In this paper, the authors presented an extension of flux-corrected transport (FCT) schemes to unstructured grids, where the spatial discretization is performed via finite elements.
Abstract: The extension of flux-corrected transport (FCT) schemes to unstructured grids is presented. The spatial discretization is performed via finite elements. In particular, triangular elements in two dimensions have been chosen. The limiting procedure is based on Zalesak's (1979) extension to more than one dimension of the FCT schemes developed by Boris and Book (1973). The resulting scheme, FEM-FCT, is capable of resolving moving and stationary shocks within two elements, and several examples are given that demonstrate the accuracy attainable, even for complicated geometries.